Positive solutions of p-Laplacian fractional differential equations with integral boundary value conditions
-
1955
Downloads
-
3221
Views
Authors
Yunhong Li
- College of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, P. R. China.
Guogang Li
- College of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, P. R. China.
Abstract
In this work, we investigate the existence of solutions of p-Laplacian fractional differential equations with
integral boundary value conditions. Using the five functionals fixed point theorem, the existence of multiple
positive solutions is obtained for the boundary value problems. An example is also given to illustrate the
effectiveness of our main result.
Share and Cite
ISRP Style
Yunhong Li, Guogang Li, Positive solutions of p-Laplacian fractional differential equations with integral boundary value conditions, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 3, 717--726
AMA Style
Li Yunhong, Li Guogang, Positive solutions of p-Laplacian fractional differential equations with integral boundary value conditions. J. Nonlinear Sci. Appl. (2016); 9(3):717--726
Chicago/Turabian Style
Li, Yunhong, Li, Guogang. "Positive solutions of p-Laplacian fractional differential equations with integral boundary value conditions." Journal of Nonlinear Sciences and Applications, 9, no. 3 (2016): 717--726
Keywords
- Multiple positive solutions
- p-Laplacian
- the five functionals fixed point theorem.
MSC
References
-
[1]
G. Chai , Positive solutions for boundary value problem of fractional differential equation with p-Laplacian operator, Bound. Value Probl., 2012 (2012), 20 pages.
-
[2]
T. Chen, W. Liu, An anti-periodic boundary value problem for the fractional differential equation with a p-Laplacian operator, Appl. Math. Lett., 25 (2012), 1671-1675.
-
[3]
T. Chen, W. Liu, Z. Hu, A boundary value problem for fractional differential equation with p-Laplacian operator at resonance, Nonlinear Anal., 75 (2012), 3210-3217.
-
[4]
X. Feng, H. Feng, H. Tan, Existence and iteration of positive solutions for third-order Sturm-Liouville boundary value problems with p-Laplacian, Appl. Math. Comput., 266 (2015), 634-641.
-
[5]
J. R. Graef, S. Heidarkhani, L. Kong, Multiple solutions for systems of Sturm-Liouville boundary value problems, Mediterr. J. Math., 2015 (2015), 16 pages.
-
[6]
Y. Guo, Y. Ji, X. Liu , Multiple positive solutions for some multi-point boundary value problems with p-Laplacian, J. Comput. Appl. Math. , 216 (2008), 144-156.
-
[7]
Y. Li, S. Lin, Positive solution for the nonlinear Hadamard type fractional differential equation with p-Laplacian, J. Funct. Spaces Appl., 2013 (2013), 10 pages.
-
[8]
S. K. Ntouyas, S. Etemad , On the existence of solutions for fractional differential inclusions with sum and integral boundary conditions, Appl. Math. Comput., 266 (2015), 235-243.
-
[9]
I. Podlubny, Fractional differential equations, mathematics in science and engineering, Academic Press, San Diego, CA (1999)
-
[10]
S. G. Samko, A. A. Kilbas, O. I. Marichev , Fractional integrals and derivatives: theory and applications, Gordon and Breach, Switzerland (1993)
-
[11]
B. Sun, W. Ge, Existence and iteration of positive solutions to a class of Sturm-Liouville-like p-Laplacian boundary value problems, Nonlinear Anal., 69 (2008), 1454-1461.
-
[12]
Y. Wang, L. Liu, Y. Wu, Extremal solutions for p-Laplacian fractional integro-differential equation with integral conditions on infinite intervals via iterative computation, Adv. Difference Equ., 2015 (2015), 14 pages.
-
[13]
X. Zhang, M. Feng, Existence of a positive solution for one-dimensional singular p-Laplacian problems and its parameter dependence, J. Math. Anal. Appl., 413 (2014), 566-582.
-
[14]
X. Zhang, L. Liu, B. Wiwatanapataphee, Y. Wu, The eigenvalue for a class of singular p-Laplacian fractional differential equations involving the Riemann-Stieltjes integral boundary condition, Appl. Math. Comput., 235 (2014), 412-422.